Resummed inclusive cross-section in ADD model at N$^3$LL+NNLO

TL;DR

This paper computes high-order quantum corrections and resummations for spin-2 particle production in the ADD model at the LHC, significantly reducing theoretical uncertainties in the predicted cross-sections.

Contribution

It provides the first complete three-loop soft-plus-virtual corrections and N$^3$LL resummed predictions for spin-2 production in the ADD model, enhancing precision for collider phenomenology.

Findings

Reduced scale uncertainties to about 2% at high invariant mass.

Quantified the impact of three-loop corrections on di-lepton mass distribution.

Provided estimates of PDF uncertainties relevant for experimental searches.

Abstract

We present three loop soft-plus-virtual (SV) corrections to the spin-2 production at the Large Hadron Collider (LHC). For this calculation, we make use of the recently computed quark and gluon three loop form factors for the spin-2 production, the universal soft-collinear coefficients as well as the mass factorization kernels. The SV coefficients are presented up to next-to-next-to-next-to leading order (N$^3$LO). We also use these coefficients at three loops to compute the resummed prediction for inclusive cross-section to next-to-next-to-next-to leading logarithmic accuracy (N$^3$LL) matched to next-to-next-to leading order (NNLO). We use the standard technique to derive the Mellin N-dependent coefficients and also the N-independent coefficients to achieve the resummation using the minimal prescription matching procedure. Considering the spin-2 propagator in the large extra dimensional (ADD) model, we also study the numerical impact of these three-loop SV corrections as well as the resummed predictions on the di-lepton invariant mass distribution at the 13 TeV LHC. We find that the conventional scale uncertainties in the NNLO+N$^3$LL resummed results substantially get reduced to as low as 2\% in the high invariant mass region. We also estimate the PDF uncertainties in our predictions that will be useful in the experimental searches for large extra dimensions.